Least Common Multiple (LCM) of 48 and 77
The least common multiple (LCM) of 48 and 77 is 3696.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 48 and 77?
First, calculate the GCD of 48 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 48 ÷ 77 = 0 remainder 48 |
| 2 | 77 ÷ 48 = 1 remainder 29 |
| 3 | 48 ÷ 29 = 1 remainder 19 |
| 4 | 29 ÷ 19 = 1 remainder 10 |
| 5 | 19 ÷ 10 = 1 remainder 9 |
| 6 | 10 ÷ 9 = 1 remainder 1 |
| 7 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 82 | 6806 |
| 195 and 112 | 21840 |
| 133 and 62 | 8246 |
| 172 and 30 | 2580 |
| 13 and 153 | 1989 |